The game starts with an integer, , that's used to build a of distinct integers in the inclusive range from to (i.e., ).
Alice always plays first, and the two players move in alternating turns.
During each move, the current player chooses a prime number, , from . The player then removes and all of its multiples from .
The first player to be unable to make a move loses the game.
Alice and Bob play games. Given the value of for each game, print the name of the game's winner on a new line. If Alice wins, print Alice; otherwise, print Bob.
Note: Each player always plays optimally, meaning they will not make a move that causes them to lose the game if some better, winning move exists.
The first line contains an integer, , denoting the number of games Alice and Bob play.
Each line of the subsequent lines contains a single integer, , describing a game.
for of the maximum score
For each game, print the name of the winner on a new line. If Alice wins, print Alice; otherwise, print Bob.
Sample Input 0
Sample Output 0
Alice and Bob play the following games:
We are given , so . Because Alice has no valid moves (there are no prime numbers in the set), she loses the game. Thus, we print Bob on a new line.
We are given , so . Alice chooses the prime number and deletes it from the set, which becomes . Because Bob has no valid moves (there are no prime numbers in the set), he loses the game. Thus, we print Alice on a new line.
We are given , so . Alice chooses the prime number and deletes the numbers and from the set, which becomes . Now there are two primes left, and . Bob can remove either prime from the set, and then Alice can remove the remaining prime. Because Bob is left without a final move, Alice will always win. Thus, we print Alice on a new line.